Question

Can I prove convergence of and show the sum $\sum_{n=1}^{\infty} (z-1){z}^{n}$ where $|z|<1$ by assuming $z$ to be a complex number?

score 58 · Answer 1 · 2026-05-14 17:06:26

58

Views

Can I prove convergence of and show the sum $\sum_{n=1}^{\infty} (z-1){z}^{n}$ where $|z|<1$ by assuming $z$ to be a complex number?

Published on 14 May 2026 - 17:06

score 78 · Answer 2 · 2026-04-12 10:26:59

78

Views

Does the adaptive cruise control system involves very complex calculus for a high school student?

Published on 12 Apr 2026 - 10:26

score 46 · Answer 3 · 2026-04-15 21:22:20

46

Views

Connectedness of the set $\{(z,w)\in S^3\subset \Bbb C^2:z^m+w^n=0\}$ where $m,n\in \Bbb N$

Published on 15 Apr 2026 - 21:22

score 299 · Answer 4 · 2026-04-09 05:30:18

299

Views

Proof of Niven's theorem

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score 138 · Answer 5 · 2026-04-10 05:59:41

138

Views

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Published on 10 Apr 2026 - 5:59

score 117 · Answer 6 · 2026-04-09 04:16:49

117

Views

An integral involving trigonometric and exponential function

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score 2.5k · Answer 7 · 2026-04-11 15:57:15

2.5k

Views

Complex number - arctan

Published on 11 Apr 2026 - 15:57

score 99 · Answer 8 · 2026-04-12 22:05:19

99

Views

Solving a complex trigonometric equation

Published on 12 Apr 2026 - 22:05

score 120 · Answer 9 · 2026-04-16 22:39:31

120

Views

Prove $\arg(zw) = \arg ((z+w)^2)$ given that $|z| = |w|$

Published on 16 Apr 2026 - 22:39

score 1k · Answer 10 · 2026-04-11 05:22:07

1k

Views

Is $\mathbb{R}^2$ a Ring?

Published on 11 Apr 2026 - 5:22

score 80 · Answer 11 · 2026-04-10 22:29:15

80

Views

De Moivre's Therom - Roots of Complex Numbers- reference angle

Published on 10 Apr 2026 - 22:29

score 65 · Answer 12 · 2026-04-15 17:12:37

Two nonzero complex numbers such that $| z_1 + z_2 |$ = $| z_1 - z_2 |$. If $z_2 ≠ 0$, show that $\frac{z_1}{z_2}$ is a pure imaginary.

score 246 · Answer 13 · 2026-04-11 19:09:16

246

Views

Dot product between two vectors with complex components

Published on 11 Apr 2026 - 19:09

score 233 · Answer 14 · 2026-04-14 02:15:25

If $\frac{z-\alpha}{z+\alpha},(\alpha \in R)$ is a purely imaginary number and $|z|=2$, can we find value of $\alpha$ geometrically?

score 48 · Answer 15 · 2026-04-13 05:31:07

48

Views

Selecting the correct root of a complex number

Published on 13 Apr 2026 - 5:31

List Question

Can I prove convergence of and show the sum $\sum_{n=1}^{\infty} (z-1){z}^{n}$ where $|z|<1$ by assuming $z$ to be a complex number?

Does the adaptive cruise control system involves very complex calculus for a high school student?

Connectedness of the set $\{(z,w)\in S^3\subset \Bbb C^2:z^m+w^n=0\}$ where $m,n\in \Bbb N$

Proof of Niven's theorem

Is there a formula to extract the real part of a complex vector?

An integral involving trigonometric and exponential function

Complex number - arctan

Solving a complex trigonometric equation

Prove $\arg(zw) = \arg ((z+w)^2)$ given that $|z| = |w|$

Is $\mathbb{R}^2$ a Ring?

De Moivre's Therom - Roots of Complex Numbers- reference angle

Two nonzero complex numbers such that $| z_1 + z_2 |$ = $| z_1 - z_2 |$. If $z_2 ≠ 0$, show that $\frac{z_1}{z_2}$ is a pure imaginary.

Dot product between two vectors with complex components

If $\frac{z-\alpha}{z+\alpha},(\alpha \in R)$ is a purely imaginary number and $|z|=2$, can we find value of $\alpha$ geometrically?

Selecting the correct root of a complex number

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